Problem: Rewrite as a simplified fraction. ${0.20\overline{4} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 204.4444...\\ 100x &= 20.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 184}$ ${x = \dfrac{184}{900}} $ ${x = \dfrac{46}{225}} $